ANGULAR GEOMETRIC INDICES

Abstract

Topological indices (TIs) are important tools for analyzing the nature of biological and chemical networks. There are five types of TIs: Degree based
TIs, distance based TIs, eigenvalue based TIs, matching based TIs and mixed TIs. Degree based TIs are defined by using classical degree concept in graph
theory. The Zagreb and Randi´ c TIs are the most used TIs in literature. An gular geometric graph, geometric degree and angle degree notions have been
defined recently in graph theory. The angles between the atoms (vertices) and bonds (edges) are important in biology and chemistry but are not important in graph theory. In this respect, angular geometric graphs, in which the angles within this graph are important and unalterable, represent more realistic model for biological and chemical networks and molecular structures. In this study, we firstly defined angular geometric Zagreb and angular geometric Randic TIs by using geometric degree notion. We compare these novel TIs with their classical degree based counterparts TIs for the prediction of some chemical properties of octanes. It is shown that the newly defined an-
gular geometric indices do not give a higher correlation coefficients than their classical counterparts .

Keywords

• Angular degree,geometric degree,angular geometric graph

References

1. 1. M. Randi´ c: On characterization of molecular branching. J. Amer. Chem. Soc., 97 (23) (1975), 6609–6615.
2. 2. I. Gutman , N. Trinajsti´ c: Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett., 17 (1971), 535-538.
3. 3. I. Gutman, B. Ruˇ sˇ ci´ c, N. Trinajsti´ c, C. F. Wilcox: Graph theory and molecular orbitals, XII. Acyclic polyenes. J. Chem. Phys., 62 (1975), 3399–3405.
4. 4. S. Ediz: A note on angular geometric graphs. Int. J. Math. Comput. Sci., 14 (3) (2019), 631–634.
5. 5. D.B. West: Introduction to graph theory.Pearson Education Press (2001) 610 pages, USA.
6. 6. I. Gutman, K. C. Das: The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 50 (2004) 83–92.
7. 7. S. Nikoli´ c, G. Kovaˇ cevi´ c, A. Miliˇ cevi´ c, N.Trinajsti´ c: The Zagreb indices 30 years after. Croat. Chem. Acta 76 (2003) 113–124.